I have a list of ranked items and the factors that the group used to create the rankings (like college rankings: 1, 2, 3...), and I'd like to reverse engineer their methodology.

Here's what I tried...

  • I took the standard score of each factor (factor value - mean / standard deviation).
  • I assigned coefficients to each factor and added up all these products to create a score.
  • I used the scores to rank the items and compared these rankings to the real rankings, trying to minimize the difference.
  • Rinse and repeat by changing the coefficients.

This is a crude method and I am very new to this. I was wondering what the best way is to figure out how this group weighted the factors to create the rankings.


Depending on the complexity of the ranking scheme, this might be more or less difficult, but if you have all the inputs and the outputs, it is very possible.

Start by plotting your data and try to see if you can see a pattern, or any obvious correlation, even though not necessarily linear. Do that for each variable.

You can also look at the distribution of your variables (what you call factors) for each of your rank, and see how they differ.

Once you have a better understanding on the relationship between the dependent variable (rank) and the independent variables (factors), then you can either:

  • Come up with the model right there
  • Apply a machine learning algorithm (linear/polynomial regression, decision trees, etc.) which will learn the model's parameters for you. Which one you chose will depend on your analysis.

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